SOLUTION: A boy and his sister took it in turns to stand on a weighing machine with their pet dog. The brother and sister together weighed 85kg. The boy and the dog weighed 60.5kg. The girl

Question 135048: A boy and his sister took it in turns to stand on a weighing machine with their pet dog. The brother and sister together weighed 85kg. The boy and the dog weighed 60.5kg. The girl and the dog weighed 49.5kg. Find the weighed in kilograms of the brother, the sister and their pet dog.
Found 2 solutions by checkley77, Earlsdon:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
x+y=85
x+d=60.5
y+d=49.5
-----------------------
x+y+2d=110
seeing as x+y=85 we now replave (x=y) with 85
85+2d=110
2d=110-85
2d=25
d=25/2
d=12.5 kg. is the weight of the dog.
x+12.5=60.5
x=60.5-12.5
x=48 kg for the boy.
y+12.5=49.5
y=49.5-12.5
y=37 kg for the sister.
proofs:
48+37=85
85=85
48+12.5=60.5
37+12.5=49.5

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let B = weight of the boy, S = the weight of his sister, and D = the weight of the dog.
1) B+S = 85 kg.
2) B+D = 60.5 kg.
3) S+D = 49.5 kg.
Now you have a system of three equations in three unknowns.
Rewrite equation 1) as: B = 85-S and substitute this into equation 2).
2a) (85-S)+D = 60.5 kg.
Rewrite equation 3) as: D = 49.5-S and substitute this for D in 2a).
2b) (85-S)+(49.5-S) = 60.5 kg. Simplify and solve this for S.
85-S+49.5-S = 60.5
134.5-2S = 60.5 Subtract 134.5 from both sides.
-2S = -74 kg Now divide both sides by -2.
S = 37 Kg. This is the sister's weight.
From equation 1) written as: B = 85-S, we get:
B = 85-37 = 48 Kg. This is the boy's weight.
From equation 3) rewritten as: D = 49.5-S, we get:
D = 49.5-37 = 12.5 Kg. This is the dog's weight.

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